Nonexotic Neutral Gauge Bosons

Adam R. Hopper (Yale); Bogdan A. Dobrescu (Fermilab); Thomas Appelquist (Yale)

REVIEW

Nonexotic Neutral Gauge Bosons

Thomas Appelquist (Yale), Bogdan A. Dobrescu (Fermilab), Adam R. Hopper (Yale)

High Energy Physics - Phenomenology · Submitted 4 Dec 2002 · 25 references

Pith's verdict: A careful, honest EFT map of anomaly-free Z' charges and the bounds on them; the classification is the durable part, the collider numbers are explicitly estimates.

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arXiv IDhep-ph/0212073 (version 3)

Pith IDJJTZ5E5P, Pith's permanent record of this paper and its review

CitationAdam R. Hopper (Yale), Bogdan A. Dobrescu (Fermilab), Thomas Appelquist (Yale). "Nonexotic Neutral Gauge Bosons." arXiv:hep-ph/0212073 (2002). https://pith.science/paper/JJTZ5E5P

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Editor's note

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Worth your time, but read it for the classification, not the numbers. The durable contribution is Section 3: with generation-independent charges, no new SM-charged fermions, and the top Yukawa fixed, anomaly cancellation leaves a two-parameter family, and the general family needs at least three right-handed neutrinos. The operator analysis in 3.2-3.3 showing which Dirac and Majorana masses survive for each n and each z_k assignment is careful and is where the paper actually adds something. The two-parameter family itself they credit to Weinberg [9] in Section 3.1, and they are right to; the novelty is the neutrino sector and the bound map, not the family. Section 2 is clean algebra: mass matrix, mixing angle, Eqs. 2.5-2.6 all check out by hand, and the observation that kinetic mixing can be rotated into the charges at any scale is a useful simplification that saves the reader from the Galison-Manohar and Babu-Kolda-March-Russell parametrizations. The Z-pole bounds are the strongest part and are honestly tree-level. On the stress-test: the S-T correlation worry is real but small. The paper states explicitly in 4.2 that there are no tree-level S or U contributions, so a one-parameter T bound is the right object; the imprecision is using the PDG marginalized T rather than a constrained fit, which moves the 0.9 TeV number at the level of the error bar, not the central value. The 'other TeV physics' caveat is standard and the EFT framing already implies it. Where I would push back harder than the reader does is Section 4.1: the LEP narrow-resonance limit is obtained by rescaling an OPAL sneutrino limit, and the spin-1 versus spin-0 comparison is one asserted sentence. That is the softest thing in the paper, and the 10^-2 to 10^-3 coupling window inherits it. The 480 GeV Tevatron number is a Z_psi rescaling and is labelled indicative. To their credit they say so and recommend LEP redo the search. Who should read it: anyone building a Z' model who needs to know which charge assignments are actually anomaly-free, and anyone who wants a defensible citation for the 1 TeV Z-pole bound. Send it out. The referee should press on the sneutrino-to-Z' translation and on whether the T bound survives a constrained fit, but neither threatens the paper's structure.

Referee report

Major objections (1)

[§4.2, Eq. (4.15) and Fig. 1] The T-parameter bound is obtained by comparing the model's tree-level T, computed with S = U = 0, to the PDG value T = -0.02 ± 0.13 extracted from a three-parameter S-T-U fit. Because marginalizing over S and U inflates the error on T, the quoted bound is, if anything, conservative, and the central 'of order 1 TeV' claim is robust; the manuscript should nevertheless say so explicitly, and should state that the bound assumes the Z' is the sole new physics contributing to T, since the tree-level restriction stated at the start of Section 4 covers only Z' loops and not other TeV-scale dynamics. A sentence quantifying the expected shift (the paper already notes a ~15% change from M_H = 115 to 300 GeV) would make the robustness of Fig. 1 transparent.

Minor objections (9)

[§4.3, Eqs. (4.24) and (4.25)] The numerical coefficients (0.55, -1.29) in Eq. (4.24) and (24, 60) in Eq. (4.25) are quoted without derivation; please state the approximations under which they were obtained (M_Z' ≫ M_Z, leading order in t_z^2, and the fermion content retained) so that the reader can reproduce them.
[§4.1, Eq. (4.6) and the OPAL translation] The conversion of the OPAL limit λ232 < 0.02 on a scalar tau-sneutrino into a limit on z_l g_z for a spin-1 Z_B-L ignores spin, angular distribution, and interference; the paper acknowledges the roughness and cross-checks against Eq. (4.6), but a sentence on the expected size of the correction would strengthen the estimate.
[§3.3, Eq. (3.9)] The solution z1 = z2 = -(4/5)z3 is stated without intermediate steps; a one-line derivation noting that the cubic implied by Eqs. (3.3)-(3.4) has a double root at z1 = z2 = z3 and a third root at z1 = z2 = -(4/5)z3 would let the reader verify it.
[§4.1] The branching fractions 18/37, 10/37, and 9/37 are quoted for M_Z' < 2m_t; naive chiral counting with N_c = 3 gives 18:12:9, so please state whether QCD corrections, the b-quark threshold, or phase-space factors account for the difference in the hadronic fraction.
[References] Reference [24] (Burgess et al.) appears in the reference list but I could not locate a citation in the text; please check.
[§2] The Z' is introduced as 'the heavy neutral gauge boson not yet discovered,' but Section 2 subsequently allows M_Z' < M_Z; suggest 'the second neutral gauge boson' to avoid the tension.
[§4.2] The sentence 'T is greater (lesser) than zero for M_Z lesser (greater) than M_Z'' is awkward; suggest 'T > 0 when M_Z < M_Z' and T < 0 when M_Z > M_Z'.'
[Figs. 1 and 2] The captions refer to 'the region allowed by Eq. (2.6)' and 'the lightly shaded area' without stating the shading convention in the caption itself; please make the figures self-contained.
[§3.4, Eq. (3.11)] The relation zu/zq = 4 - 3g_R^2/g_Y^2 is stated without derivation; a sentence connecting it to the covariant derivatives of U(1)_R × U(1)_{B-L} would help the reader.

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The paper

The paper claims

Any new neutral gauge boson with ordinary-strength couplings must be heavier than about a TeV, and the paper shows the bound is set by how strongly that boson couples to the Higgs doublet rather than by any particular grand-unified model.

The reading

The paper asks a narrow but consequential question: if a new electrically neutral, color-singlet gauge boson exists, what can be said about it without committing to a particular grand-unified or string model? The authors show that the measured electric charges of the observed fermions force any such boson to be described by the standard hypercharge group plus one extra $U(1)_z$, written in a basis where the two gauge fields have no kinetic mixing. Under the assumptions of generation-independent charges and no new fermions charged under the Standard Model, anomaly cancellation plus the requirement that quarks and leptons can get masses leaves a two-parameter family of charge assignments, provided at least three right-handed neutrinos exist. The payoff is a set of bounds: for generic charges and a coupling of electromagnetic strength, Z-pole data push the new boson above roughly a TeV, while in the $B-L$ case, where the $Z$ and $Z'$ do not mix at tree level, direct searches give a weaker but cleaner bound. The practical message is that a sufficiently weakly coupled $Z'$ can hide at almost any mass, so null searches do not close the door.

What carries the argument

The argument is carried by a $3$ by $3$ mass-square matrix for $(B_Y, W^3, B_z)$ built from the two scalar vacuum expectation values, with a mixing angle $theta'$ satisfying $tan 2theta' = 2 z_H t_z cos theta_w / [(r + z_H^2) t_z^2 cos^2 theta_w - 1]$, where $t_z = g_z/g$ and $r = v_phi^2/v_H^2$. Diagonalizing it gives the $Z$ and $Z'$ masses and shows that the photon coupling is unchanged, which is what identifies the extra group as hypercharge plus a new $U(1)_z$. The precision constraint is then packaged into the oblique parameter through $alpha T/(1+alpha T) = (1/2)[1 - M_Z^2/M_{Z'}^2 - sqrt{(1 - M_Z^2/M_{Z'}^2)^2 - 4 z_H^2 t_z^2 cos^2 theta_w M_Z^2/M_{Z'}^2}]$, which depends on only two new quantities, $M_{Z'}$ and $z_H t_z$. Shifts in $Gamma_Z$ and $A_e$ are computed the same way, giving the coefficients $0.55 z_H^2 - 1.29 z_H z_q$ and $24 z_H^2 + 60 z_H z_q$ in the heavy-$Z'$ limit. On the theory side, the anomaly conditions $z_l = -3z_q$, $z_d = 2z_q - z_u$, $z_e = -2z_q - z_u$ reduce the charge assignment to the two-parameter family, and the mixed gravitational and cubic anomaly conditions fix the right-handed neutrino charges up to discrete choices.

Extended reading notes

Core claim

The central claim is that the mass and couplings of a new neutral gauge boson are not free once one insists that the theory be anomaly-free, give the observed fermions their masses, and respect generation independence. The allowed $U(1)_z$ charges of quarks and leptons collapse to two real parameters, $z_q$ and $z_u$, with the Higgs charge fixed at $z_H = z_u - z_q$ by the top Yukawa coupling; the right-handed neutrino charges are constrained but not unique, and at least three such neutrinos are needed for the general family. From that family the authors derive experimental bounds. For generic charges with $g_z$ of electromagnetic strength, the strongest limit comes from Z-pole observables, namely the $T$ parameter, the total $Z$ width, and the left-right electron asymmetry, and puts $M_{Z'}$ at roughly $0.9$ to $1.2$ TeV at 95% confidence. For $B-L$ charges, where $z_H = 0$ and the tree-level $Z$ to $Z'$ mixing vanishes, the Z-pole bounds evaporate and direct production takes over: about $480$ GeV from CDF Run I dileptons and about $300$ GeV from LEPII for a coupling near $e$. If $g_z$ is one or two orders of magnitude below $e$, most of these bounds are satisfied for essentially any $Z'$ mass.

Load-bearing premise

The TeV-scale bound assumes the new boson is the only new physics entering the electroweak precision observables, computed at tree level with the Higgs mass fixed near $115$ GeV; any additional TeV-scale dynamics in the same sector would shift the quoted number, and the paper does not quantify that shift.

Editorial extensions

If this is right

A $Z'$ with generic charges and a coupling of electromagnetic strength is excluded below roughly $0.9$ to $1.2$ TeV, so direct searches in that region need not be mounted for such models.
A $B-L$ $Z'$ with electromagnetic-strength coupling is excluded below about $480$ GeV by CDF Run I dilepton data, and below about $300$ GeV by LEPII.
Because the tree-level mixing vanishes exactly when $z_H = 0$, the Z-pole bound is really a bound on the product $z_H g_z$, and it weakens continuously as that product shrinks.
Model builders are not restricted to the familiar $E_6$-inspired charge assignments: any $(z_q, z_u)$ pair is viable once three right-handed neutrinos are added, and each choice implies a different set of higher-dimensional operators for neutrino masses.
A $Z'$ coupling one or two orders of magnitude below $e$ survives all current bounds at nearly any mass, including masses below $M_Z$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's bound is best read as a constraint on the Higgs charge rather than on the $Z'$ mass alone; a future precision $T$-parameter or $Gamma_Z$ measurement tighter by a factor of a few would translate directly into a sharper limit on $z_H g_z$ across the whole mass range.
If the singlet scalar that breaks $U(1)_z$ also couples to the Higgs through a portal, its mass becomes a second free knob, and the quoted TeV number would need recomputation with that contribution to $T$ included.
The pattern of neutrino-mass operator dimensions tracks the right-handed neutrino charges $z_k$, so a future $Z'$ discovery combined with a determination of the neutrino mass ordering could over-determine the charge assignment and test the two-parameter family.
The authors explicitly recommend that LEP reanalyze its data for narrow resonances; that is a concrete, unfinished experimental task that could still turn up a light, weakly coupled $Z'$ in existing archived data.

Original abstract

We study theoretical and experimental constraints on electroweak theories including a new color-singlet and electrically-neutral gauge boson. We first note that the electric charges of the observed fermions imply that any such Z' boson may be described by a gauge theory in which the Abelian gauge groups are the usual hypercharge along with another U(1) component in a kinetic-diagonal basis. Assuming that the observed quarks and leptons have generation-independent U(1) charges, and that no new fermions couple to the standard model gauge bosons, we find that their U(1) charges form a two-parameter family consistent with anomaly cancellation and viable fermion masses, provided there are at least three right-handed neutrinos. We then derive bounds on the Z' mass and couplings imposed by direct production and Z-pole measurements. For generic charge assignments and a gauge coupling of electromagnetic strength, the strongest lower bound on the Z' mass comes from Z-pole measurements, and is of order 1 TeV. If the new U(1) charges are proportional to B-L, however, there is no tree-level mixing between the Z and Z', and the best bounds come from the absence of direct production at LEPII and the Tevatron. If the U(1) gauge coupling is one or two orders of magnitude below the electromagnetic one, these bounds are satisfied for most values of the Z' mass.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,820 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.58 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.17 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We study theoretical and experimental constraints on electroweak theories including a new color-singlet and electrically-neutral gauge boson. We first note that the electric charges of the observed fermions imply that any such Z' boson may be described by a gauge theory in which the Abelian gauge groups are the usual hypercharge along with another U(1) component in a kinetic-diagonal basis. Assuming that the observed quarks and leptons have generation-independent U(1) charges, and that no new fermions couple to the standard model gauge bosons, we find that their U(1) charges form a two-parameter family consistent with anomaly cancellation and viable fermion masses, provided there are at least three right-handed neutrinos. We then derive bounds on the Z' mass and couplings imposed by direct production and Z-pole measurements. For generic charge assignments and a gauge coupling of electromagnetic strength, the strongest lower bound on the Z' mass comes from Z-pole measurements, and is of order 1 TeV. If the new U(1) charges are proportional to B-L, however, there is no tree-level mixing between the Z and Z', and the best bounds come from the absence of direct production at LEPII and the Tevatron. If the U(1) gauge coupling is one or two orders of magnitude below the electromagnetic one, these bounds are satisfied for most values of the Z' mass.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study theoretical and experimental constraints on electroweak theories including a new color-singlet and electrically-neutral gauge boson.	contribution 0.98	0.86	0.07	asserted 0.84
s1	We first note that the electric charges of the observed fermions imply that any such Z' boson may be described by a gauge theory in which the Abelian gauge groups are the usual hypercharge along with another U(1) component in a kinetic-diagonal basis.	contribution 0.36	0.55	0.04	hedged possibility 0.98
s2	Assuming that the observed quarks and leptons have generation-independent U(1) charges, and that no new fermions couple to the standard model gauge bosons, we find that their U(1) charges form a two-parameter family consistent with anomaly cancellation and viable fermion masses, provided there are at least three right-handed neutrinos.	result 0.90	0.93	0.12	asserted 0.88
s3	We then derive bounds on the Z' mass and couplings imposed by direct production and Z-pole measurements.	contribution 0.65	0.93	0.06	asserted 0.98
s4	For generic charge assignments and a gauge coupling of electromagnetic strength, the strongest lower bound on the Z' mass comes from Z-pole measurements, and is of order 1 TeV.	result 1.00	0.84	0.24	asserted 1.00
s5	If the new U(1) charges are proportional to B-L, however, there is no tree-level mixing between the Z and Z', and the best bounds come from the absence of direct production at LEPII and the Tevatron.	result 0.99	0.65	0.12	asserted 0.99
s6	If the U(1) gauge coupling is one or two orders of magnitude below the electromagnetic one, these bounds are satisfied for most values of the Z' mass.	result 0.88	0.70	0.13	asserted 0.84

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.79.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Bounds at the 95% confidence level in the (

**Figure 2.** We note that for zHtz ≪ 1 there is an allowed region of parameter space with MZ′ < MZ

Figures reproduced from arXiv:hep-ph/0212073 by the authors.

References

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Long-lived TeV-scale right-handed neutrino production at the LHC in gauged $U(1)_X$ model
hep-ph 2019-06 conditional novelty 5.0 of 10

In the gauged U(1)_X model the maximum right-handed neutrino decay length scales as 1/m_lightest, so a lightest active neutrino mass below about 10^-5 eV yields a long-lived TeV-scale RHN with a displaced-vertex signa...
Implications of unitarity and gauge invariance for simplified dark matter models
hep-ph 2015-10 accept novelty 5.0 of 10

Requiring gauge invariance and perturbative unitarity in a fermionic dark matter model with a vector mediator forces a dark Higgs sector, and the resulting dilepton, electroweak precision and Higgs constraints are str...
Les Houches 2011: Physics at TeV Colliders New Physics Working Group Report
hep-ph 2012-03 conditional novelty 5.0 of 10

The report proposes a Dark Matter Les Houches Agreement file format, extends the Flavour and SUSY accords to dipole moments and see-saw models, and reports new tool modules for automated RGE derivation and model validation.
Light Z' Bosons at the Tevatron
hep-ph 2011-03 conditional novelty 5.0 of 10

A single leptophobic Z' near 150 GeV, with couplings tuned separately to each channel, can accommodate the Tevatron W+jj, multi-b, and top-asymmetry anomalies and double as a dark matter mediator.
Z' physics with early LHC data
hep-ph 2010-10 conditional novelty 5.0 of 10

Mapping Z-prime search limits onto a two-parameter coupling plane shows that 500 inverse picobarns of 7 TeV LHC data should exclude the standard benchmark models up to roughly 1.5 to 2.2 TeV, well beyond Tevatron reach.
A Classification of Dark Matter Candidates with Primarily Spin-Dependent Interactions with Matter
hep-ph 2010-03 conditional novelty 5.0 of 10

If dark matter scatters off nuclei primarily through spin-dependent interactions, it is naturally a Majorana fermion or a real vector boson, and its mediator lies at or below the TeV scale.
Non-universal minimal Z' models: present bounds and early LHC reach
hep-ph 2009-11 accept novelty 5.0 of 10

Among anomaly-free minimal Z' models, the muonphilic B-3L_mu variant is nearly unconstrained by electroweak precision data and is reachable in early LHC dimuon searches.
Minimal Z' models: present bounds and early LHC reach
hep-ph 2009-09 accept novelty 5.0 of 10

A three-parameter description of Z-prime models shows the early LHC can first probe new territory near 700 GeV, while heavier masses remain excluded by precision electroweak data.
Effective Theory Analysis of Precision Electroweak Data
hep-ph 2004-12 conditional novelty 5.0 of 10

A simultaneous fit of 21 flavor- and CP-conserving dimension-six operators to LEP1, SLD, LEP2, W-mass, neutrino-scattering and atomic-parity data yields a published chi-squared matrix that gives bounds on any linear c...
A Compatibility Check: Low-Scale Chiral $U(1)_X$ Theories Vs. $(g-2)_e$ Anomaly
hep-ph 2026-08 conditional novelty 4.0 of 10

Three benchmark chiral U(1)_X models cannot simultaneously explain the electron (g-2) anomaly and pass current neutrino-scattering bounds, so they are excluded as complete new-physics explanations.
Generation-separated hypercharges and dark charges: origin of flavor, neutrino masses, and dark matter
hep-ph 2026-07 conditional novelty 4.0 of 10

Generation-separated U(1) hypercharges plus a dark U(1) can generate hierarchical charged-fermion masses, seesaw/scotoseesaw neutrinos, and Z2-stabilized TeV-scale dark matter from one breaking pattern.
Kination-like Era Driven by the Effective Inflaton/Higgs Potential
astro-ph.CO 2025-05 conditional novelty 4.0 of 10

Radiative corrections to the U(1)_X Higgs inflaton produce a post-inflationary stiff era that characteristically modulates the inflationary gravitational wave spectrum, connecting the signal to the Z' boson mass and g...
Non-Standard Neutrino Interactions at Neutrino Experiments and Colliders
hep-ph 2025-05 unverdicted novelty 4.0 of 10

Collider searches are generally more constraining than neutrino measurements on simplified models of non-standard neutrino interactions, except possibly for muon-philic leptoquarks and certain heavy neutral leptons.
Enhanced pair production of heavy Majorana neutrinos at LHC
hep-ph 2017-10 conditional novelty 4.0 of 10

In the minimal U(1)_X model, the Z' boson's decay to heavy Majorana neutrinos can be enhanced by up to about 3.25 times per generation relative to its decay to charged lepton pairs, improving LHC discovery prospects.
$Z^\prime$-portal right-handed neutrino dark matter in the minimal U(1)$_X$ extended Standard Model
hep-ph 2016-11 conditional novelty 4.0 of 10

Generalizing the B-L right-handed-neutrino dark matter model to a one-parameter U(1)_X family, the authors find the mediating Z' boson must be heavier than about 2.7 TeV.
Classically conformal U(1)' extended standard model, electroweak vacuum stability, and LHC Run-2 bounds
hep-ph 2016-05 conditional novelty 4.0 of 10

Requiring the Higgs quartic coupling to stay positive to the Planck mass and applying ATLAS/CMS Run-2 Z' limits confines the classically conformal U(1)' model to 3.5 TeV < m_Z' < 7 TeV.
Dirac-Fermionic Dark Matter in $U(1)_X$ Models
hep-ph 2015-06 conditional novelty 4.0 of 10

For four anomaly-free U(1)_X extensions with a Dirac fermion dark matter candidate, the combination of LHC dilepton, direct detection, indirect detection, and muon g-2 constraints excludes dark matter below about 1 Te...
Z' Mediated Dark Matter Models for the Galactic Center Gamma-Ray Excess
hep-ph 2014-11 conditional novelty 4.0 of 10

Three classes of Z'-mediated dark matter models survive existing collider and direct-detection constraints while reproducing the Galactic Center gamma-ray excess, and one new anomaly-free axial-leptophobic U(1)' model...
Correlating lepton flavor violating $b \to s$ and leptonic decay modes in a minimal abelian extension of the Standard Model
hep-ph 2026-06 unverdicted novelty 3.0 of 10

In the ABCD model, experimental upper bounds on tau to three muons, muon to electron gamma, and related LFV processes constrain branching ratios of LFV B(s) decays in hierarchical order.
$Z^\prime$ portal dark matter in the minimal $B-L$ model
hep-ph 2018-03 conditional novelty 3.0 of 10

Combining the dark matter relic density with the ATLAS 36/fb dilepton search excludes B-L Z' bosons below 3.9 TeV in the Z' portal right-handed neutrino dark matter scenario.
Evidence for and implications of a dark photon
hep-ph 2025-06 conditional novelty 2.0 of 10

A global QCD fit to deep-inelastic scattering prefers a dark photon with mass 4 to 6 GeV and mixing 0.06 to 0.12, claimed as a 6.5 sigma hint, though direct searches exclude these parameters unless extra dark matter c...
The Dark Photon
hep-ph 2020-05 unverdicted novelty 2.0 of 10

The paper surveys theoretical motivations, experimental searches, and bounds on the dark photon as a kinetically mixed gauge boson from a dark sector, covering both massive and massless cases along with related milli-...
Stable Massive Particles at Colliders
hep-ph 2006-11 accept

The paper is a comprehensive review of collider searches for stable massive particles, their theoretical motivations, detector signatures, and the resulting mass and cross-section limits.

How later papers used it

111 later papers cite it

Evidence: substantial. 111 of the citing papers share no author with it, and 10 of those carry a confident label from Pith's citation classifier.

Pith read 17 of the 150 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 1 used its method or tool and 1 cited it as support.

Uses its method or tool 1 of 2 papers with this label

Used this paper's framework for anomaly-free U(1) extensions of the standard model.

Non-Standard Neutrino Interactions at Neutrino Experiments and Colliders (2025) · 0.83 · paraphrased: the licence does not allow quoting

Cites it as support 1 paper

Said that the absence of significant Z-Z' mixing, ensured by its charge assignments, is consistent with electroweak precision measurements, citing this paper as support.

Neutrino mass generation via the inverse seesaw mechanism in a $U(1)_{B-L}$ gauge extension (2025) · 0.96 · paraphrased: the licence does not allow quoting

How the literature uses it

96 arXiv papers cite this in 131 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 87 sentences without a confident label

Uses its method or tool 2 papers

Using the narrow-width approximation, the cross section can be expressed as [ref] [equation] Because the branching ratio of $Z'→NN$ is independent of the new gauge coupling $g'$, the cross section of $μ^+μ^-→Z'γ→NNγ$ is proportional to $e^2g^'2$, while the cross section of off-shell process $μ^+μ^-→Z ^'(*)γ→NNγ$ is proportional to $e^2g^'4$.

Heavy Neutral Leptons in Gauged $U(1)_{L_\mu-L_\tau}$ at Muon Collider · With Associated Photon · 0.85
We use the framework for anomaly-free U(1) extensions of the SM from Ref. [ref] , with an interaction Lagrangian of the form

Non-Standard Neutrino Interactions at Neutrino Experiments and Colliders · Gauge boson with axial charges · 0.83

Uses its data or values 4 papers

According to Ref. [ref] , the results of the LEPII experiment show that $Z'$ is either heavier than the largest center-of-mass energy ($209$) or $|z_ℓg_z| ≲10^-3$.

Exclusion bounds for neutral gauge bosons · Direct Z-prime boson searches · 0.95
Searches at LEP, which would produce the $Z'$ in conjunction with the photon, give a generic bound around $≲10^-2$ [ref] , provided that the mass of the $Z'$ is not too close to the center-of-mass energy of any of the LEP runs, namely $√(s) =130, 136, 161, 172, 183$ GeV, which is always true in the case of the light $Z'$.

Anomalous $Z'$ and Diboson Resonances at the LHC · Existing Constraints on Light Z's and the LHC Searches · 0.83
$Z'$ couples to the usual fermions via the Lagrangian, ℒ⊃-g_N [N(f_L) f̅_L ^μf_L+N(f_R) f̅_R ^μf_R] Z'_μ.If $m_Z'$ is smaller than the highest collision energy of the LEPII, $√(s)=209$ GeV, it may be resonantly produced at the LEPII, and the agreement with the standard model indicates that $g_N≲10^-2$, up to a factor of $δ$ [ref] .

Dequantization of electric charge: Probing scenarios of cosmological multi-component dark matter · Collider searches for $Z'$ · 0.80

Compares with it 2 papers

As we will later see, this $∼10^-2$–$10^-3$ reach is comparable to the LHC reach to similar scenarios due to the direct production of the $Z'$ [ref] as well as to the LEP and Tevatron sensitivities to similar scenarios [ref] .

Anomalous $Z'$ and Diboson Resonances at the LHC · Introduction · 1.00
For masses of the $Z'$ boson $M_Z' = 1, 2 TeV$, the constraints obtained from the ATLAS collaboration [ref] are stronger than the cosmological ones, while for $M_Z' = 5 TeV$ the cosmological limit on $g'$ is stronger than the one from colliders, which comes from LEP [ref] .

Constraining UV freeze-in of light relics with current and next-generation CMB observations · Right-handed neutrinos in model · 0.91

Cites it as background 31 papers

Besides the so-called Sequential Standard Model (SSM) and the $E_6$-inspired models, which have been already extensively studied [ref] , there is a more general and model-independent parametrisation of a $Z'$ boson and its couplings, as proposed in [ref] , generally referred to as "minimal" $Z'$ model.

Indirect Sensitivity to Heavy Z' Bosons at a Multi-TeV e+e- Collider · Indirect sensitivity · 0.97
A number of anomaly free $U(1)_X$ symmetries have been explored, including $(B-L)$, ($B-3L_i)$, $(B_i-3L_j)$, and $(L_i-L_j)$, as well as their linear combinations [ref] .

Generalized Chiral $U(1)_{B-L}$: Towards a Less Constrained $Z'$ and Dark Matter · Introduction · 0.96
The anomaly free, $B-L$ gauge invariant Lagrangian density describing the interactions between a $Z'$ boson and Standard Model fermions takes the form [ref]

Constraints on the $U(1)_{B-L}$ model from global QCD analysis · $U(1)_B-L$ symmetry · 0.80

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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